Geometric Construction: Finding the Correct Median in a Triangle

Triangle Medians with Midpoint Identification

Look at triangle ABC below.

Which is the median?

αααAAABBBCCCDDDEEE

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at triangle ABC below.

Which is the median?

αααAAABBBCCCDDDEEE

2

Step-by-step solution

To solve this problem, we must identify which line segment in triangle ABC is the median.

First, review the definition: a median in a triangle connects a vertex to the midpoint of the opposite side. Now, in triangle ABC:

  • Point A represents the vertex.
  • Point E lies on line segment AB.
  • Line segment EC needs to be checked to see if it connects vertex E to point C.

From the diagram, it appears that E is indeed the midpoint of side AB. Thus, line segment EC connects vertex C to this midpoint.

This fits the definition of a median, verifying that EC is the median line segment in triangle ABC.

Therefore, the solution to the problem is: EC \text{EC} .

3

Final Answer

EC

Key Points to Remember

Essential concepts to master this topic
  • Definition: A median connects any vertex to the midpoint of the opposite side
  • Method: Find the midpoint on side AB, then draw line from vertex C
  • Check: Verify point E is exactly halfway between vertices A and B ✓

Common Mistakes

Avoid these frequent errors
  • Confusing medians with other triangle segments
    Don't assume any line from a vertex is a median = wrong identification! Lines like AD might look important but don't connect to midpoints. Always verify the endpoint is exactly the midpoint of the opposite side.

Practice Quiz

Test your knowledge with interactive questions

Is the straight line in the figure the height of the triangle?

FAQ

Everything you need to know about this question

How can I tell if point E is really the midpoint of AB?

+

Look for visual clues in the diagram! Point E should appear exactly halfway between A and B. In this problem, the diagram shows E positioned at the midpoint of side AB.

Why isn't AD the median instead of EC?

+

Point D lies on side BC, not at its midpoint. A median must connect a vertex to the midpoint of the opposite side. AD connects vertex A to point D, but D isn't the midpoint of BC.

Can a triangle have more than one median?

+

Yes! Every triangle has exactly three medians - one from each vertex to the midpoint of the opposite side. In this problem, we're only identifying one of them.

What's the difference between a median and an altitude?

+

A median goes to the midpoint of the opposite side, while an altitude is perpendicular to the opposite side. They're completely different triangle segments with different purposes!

Does the length of EC matter for it to be a median?

+

No! The length doesn't determine if it's a median. What matters is that EC connects vertex C to point E, and E is the midpoint of side AB.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Triangle questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations